Eevee volumetrics different in render
You are correct volumetrics are a bit different in EEVEE. For some reason, emission strength is required to control the volume. As you can see, I upped the emission strength, then plugged the volume into the emission color, to make it constrained to the cloud. Have a try. You might need to  play with the values a little to get it just right in your scene, but it's a start.